This invention generally relates to tuning musical instruments and more specifically to apparatus which simplifies tuning procedures.
Conventionally, a person listens to a reference note and adjusts a musical instrument until its note seems consonant with the reference note. Consciously, or not, the person tunes a note for a zero beat with the reference note, usually at some coincident harmonic or partial of either one or both the notes.
This type of tuning, known as Interval Tuning, is possible because a conventional scale is based upon mathematical relationships. In practice, however, pianos and other stringed instruments do not follow simple mathematical rules. The overtones, or partials, generated by a given note are more than integral multiples of the fundamental. This deviation, termed "stretch", may be defined as the difference between a partial and corresponding harmonic (e.g., the second partial and theoretical second harmonic frequency) or a note. Stretch is significant. In a piano, for instance, the second partial from a string averages 2.002 to 2.006 or more times the fundamental frequency. Thus, if the fundamental notes are tuned mathematically, stretch causes a piano to sound out of tune.
Therefore, pianos and similiar instruments must be tuned differently. The general approach is a complex, iterative process in which a tuner tries to reduce errors to a minimum step-by-step. Basically, a piano tuner starts tuning a piano in a "temperament octave" by adjusting a first note to a reference frequency. He adjusts the remaining notes in the temperament octave by listening to partials of third, fourth and fifth intervals. For example, in striking an interval of a third with a previously tuned lower note, the tuner adjusts the upper note while listening to the beat between the fifth partial of the lower note and the fourth partial of the upper note. He assumes the proper relationship exists when he obtains a predetermined beat frequency between these coincident partials.
Listening to these partials reduces errors at the fundamental frequency because the partial errors are multiplied in terms of actual frequency differences. That is, a 4 Hz error at the fourth partial represents only a 1 Hz error at the fundamental. Also, the use of partials inherently tends to compensate for piano stretch. However, the process is not perfect and the tuner usually checks the temperament using different intervals and retunes it as necessary to minimize the tuning errors.
Once the tuner completes the temperament octave, he tunes other notes by comparing partials while playing octave intervals. He may, for example, listen to the beat between the fourth partial of a lower, tuned note and the second partial of the upper note while adjusting string tension for the upper note. Lower notes are tuned similarly.
Most piano notes have two or three strings. During the foregoing interval timing procedure, the tuner damps out strings so only one string actually sounds when a hammer strikes all the strings associated with that note. After the tuner completes the interval tuning procedure, he must tune the other strings for each note to be in unison with the first string comparing corresponding partials of two strings associated with a given note.
As may be apparent, however, the entire procedure requires that a note sustain long enough to enable the tuner to determine the beat frequency. Obviously, the longer the interval the note sustains, the more accurately the tuner can determine the beat frequency. In tuning, each note struck sounds until it dies out naturally or the key is released. By "dying out", I mean that the note can no longer be heard.
Although there are several tuning aids, no one aid has wide acceptance. In one, a high frequency oscillator produces an output clock signal at a selected frequency. A series of frequency dividers and an octave selector switch provide a means for generating a reference signal at a selected subharmonic frequency. The tuning aid combines this reference signal and an audio signal representing the note being tuned either to generate an audible beat note or to deflect a pointer on an indicating meter. Unfortunately, these aids lose accuracy as the tuned note comes into frequency with the reference. When the beat rate decreases below 20 Hz and especially 1 Hz, the audible beat note becomes inaudible. Similarly, an indicating meter uses a frequency-to-current converter so the current level goes to zero at a zero beat. As the current approaches zero, the visual indication becomes less accurate. Both types of display, therefore, lose accuracy at the very time it is most necessary.
In another unit, the tuner attaches a piezoelectric transducer to a particular string or a sounding board to produce a corresponding electrical signal that is applied to the vertical deflection plates of a cathode ray tube. A selector switch, crystal controlled oscillator and a series of frequency dividers generate a selected reference signal which energizes the horizontal deflection plates of the tube. In using this circuit, one apparently assumes, erroneously, that a piano generates a constant, repetitive wave form. In fact, a piano string generates an extremely complex wave form with a fundamental frequency and partials slightly out of tune with each other but often of the same magnitude. Furthermore, the component frequencies are not necessarily constant in relative magnitude because a string vibrates in many modes, each with its own damping constant. These factors cause the waveform to change continuously, so the display is difficult to interpret.
Another problem relates to dynamic response. Initially, the amplitude of the signal is sufficient to drive the display off the screen. As the tone dies out, the input to the vertical deflection plates falls below the minimum level necessary for generating a usable display. An obvious solution is installing a variable gain amplifier to maintain the output at a constant value. However, a circuit which provides satisfactory results over the wide range of conditions and waveforms which the piano generates is difficult to attain in practice. If the variable gain circuit actually tracks the decay, it may follow the waveform and provide a dc output signal. Therefore, this solution is not practicable especially in view of the non-linear parameters or conditions and the short interval for a readable display. This effective dynamic range further complicates tuning because adjusting a string while monitoring the display is very difficult.
Still another tuning aid receives the audio signal from a piano and generates a corresponding electrical signal to energize the blanking or Z axis circuitry of a cathode ray tube. A circular generator energizes X and Y axis deflection plates with a reference frequency so the electron beam describes a circle on the screen. If a note is in tune with the reference, the audio signal blanks and unblanks the electron beam during the same part of each revolution to thereby display one arcuate segment. A second harmonic input signal produces two such arcuate segments; a third harmonic input signal, three segments; and so forth. If a given note is not exactly harmonically related to the reference, the segments rotate. The direction of rotation indicates whether the note is sharp or flat while the speed of rotation indicates the difference in frequencies. As notes in the upper piano produce a display with a number of segments, the spaces between adjacent sectors diminish; and the absolute frequency deviation which produces a persistent display tends to decrease. Furthermore, alternately blanking and unblanking the beam produces an indefinite segment termination on the screen. When the frequency deviation is small, the indefinite termination makes it difficult to determine whether the edges of the segment are moving. When notes in the lower range of the piano are tuned, the tuner must try to adjust while the tuning aid responds to harmonics, since subharmonics of the reference frequency generate complete circles on screen.
Apparently, another reason professional piano tuners are reluctant to use prior aids is that each piano is tuned uniquely, so a generalized tuning aid that responds to the fundamental frequency of the note being tuned does not really help the tuner. The unique quality of each piano stems from its construction, string length, wear on hammers, and myriad other factors. As a result, piano tuners continue to work conventionally and do not place any significant reliance on mechanical aids.
Therefore, it is an object of my invention to provide a tuning aid which is readily adapted for tuning a wide variety of instruments.